It is possible to restrict the plotting region by using `RegionFunction`.  However, it is also necessary to construct a concave hull of the data, and use a higher `MaxPlotPoints` when making the contour plot.  Using RunnyKine's code from [here](https://mathematica.stackexchange.com/a/88769/9490) to construct the region,



    dat = Flatten[
       Import["https://dl.dropboxusercontent.com/u/659996/odd-data.m"], 1];
    reg = alphaShapes2D[DeleteDuplicates@dat[[All, ;; 2]], .33];
    RegionPlot[reg]

[![enter image description here][1]][1]

We can now get the proper contour plot,

    Show[
     ListContourPlot[dat, PlotLegends -> Automatic, PlotRange -> All, 
      RegionFunction -> Function[{x, y, z}, RegionMember[reg, {x, y}]], 
      MaxPlotPoints -> 100],
     ListPlot@dat[[All, ;; 2]]
     ]

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/1i50z.png
  [2]: https://i.sstatic.net/GO5eo.png